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3D Numerical Modeling of Umbrella Cloud Growth and Regimes

Yujiro J. Suzuki

Abstract

Large-scale explosive volcanic eruptions produce clouds that expand horizontally in the stratosphere as density gravity currents, forming "umbrella clouds." The area of an umbrella cloud serves as a key indicator of eruption intensity. In the case of steady intrusions in a windless environment with the constant Brunt-Väisälä frequency, the horizontal expansion of density gravity currents follows a scaling law based on the elapsed time and the volumetric inflow rate. The flow regimes vary depending on the balance of forces, each characterized by distinct power-law exponents for spreading time (Poret et al., 2016). In contrast, umbrella clouds spread in a wind field with the Brunt-Väisälä frequency changing with height. Umbrella cloud growth also depends on the volcanic plume dynamics. We conducted direct numerical simulations to explore umbrella cloud growth using the three-dimensional pseudo-gas model SK-3D (Suzuki et al., 2005). Parameter studies were performed by varying eruption rates, atmospheric structures, and wind velocities. The results revealed distinct flow patterns, such as umbrella clouds from stable plumes and co-ignimbrite ash plumes generated by pyroclastic density currents. Multiple power-law exponents, including 4/3 and 10/9, were identified, reflecting different flow regimes such as buoyancy-inertial and turbulent drag-dominated intrusion regimes. Interestingly, these power laws did not always correspond directly to flow patterns or specific atmospheric conditions. We summarize the relationships between eruption conditions and power-law exponents and discuss the implications for understanding umbrella cloud regimes.